Tunable quantum microwave to optical conversion system

ABSTRACT

A electronic method, includes receiving, by a graphene structure, a microwave signal. The microwave signal has a driving voltage level. The electronic method includes generating, by the graphene structure, optical photons based on the microvolts. The electronic method includes outputting, by the graphene structure, the optical photons.

BACKGROUND

There are several techniques that couple quantum photonics and quantummicrowave systems. This includes atomic interface techniques,opto-mechanical techniques, and electro-optic (EO) techniques. Forexample, EO techniques provide for wide operation bandwidths which aretunable and scalable. This allows the EO technique to modulate anoptical input pump by a driving microwave signal which also generates anupper and lower sideband. The lower sideband creates noise upon theconversion process as the conversion of a pump photon into a lower sideband photon may generate a microwave photon. To minimize noise, a singlesideband (SSB) scheme is implemented. However, in such EO techniques,large microwave voltages (e.g., millivolts) are required to conduct themicrowave-to-optical conversion. While, high Q-factor resonators may beused to enhance the EO techniques, such resonators limit the tenabilityof the conversion process. Currently, there is no effective techniquethat uses voltages less than millivolts which also reduces noise toconduct optimal microwave-to-optical conversion.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram of an example model graphene structural design;

FIG. 2 is a diagram of an example model capacitance design;

FIGS. 3 and 4 are example electronically generated graphs;

FIGS. 5 and 6 are example electronically generated graphs;

FIG. 7 is an example electronically generated graphs;

FIGS. 8 and 9 are example electronically generated graphs;

FIG. 10 is an example device;

FIG. 11 is an example system; and

FIG. 12 is an example system.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The following detailed description refers to the accompanying drawings.The same reference numbers in different drawings may identify the sameor similar elements.

Systems, devices, and/or methods described herein may provide forconversion of microwave signals to optical photons using a multilayergraphene structure design as a tunable modulator. In embodiments,graphene layers (e.g., in a graphene structure) are electronicallyconnected and pumped by an optical field. In embodiments, a drivingmicrowave signal modulates the optical input pump. In embodiments, upperand lower sidebands are generated. In embodiments, to generate low noiseconversion, the lower sideband is suppressed by the multilayer graphenedestruction resonance which is a function of the graphene structuredesign. Accordingly, the quantity of photons generated from a lowerquantity of microwave signals is increased. Also, a frequency-tunableoperation is also attained over a vast frequency range (e.g., 1 to 60GHz (gigahertz)) by modifying the optical frequency range. Additionally,the graphene structure may allow for reduced pump intensity levels(e.g., 10⁸ ν₀ ²/g²), quantum driving voltages, and large signal-to-noiseratios (SNR).

As such, a more efficient micro-wave-to-optical conversion is describedherein. In embodiments, the graphene layers, within a graphenestructure, are connected in an interdigital configuration and,electrically, function as a capacitor and, optically, as a periodicmedium. In embodiments, a destruction resonance of the medium is fixedby setting it a particular value and the values of the optical pumpfrequency and the microwave signal are varied. In embodiments, suchvalues results in the lower sideband frequency to be at the destructionresonance value. Thus, for the described methods, structures, andsystems, at greater rates of conversion of microwave-to-optical isachieved with (1) low driving voltages (e.g., 1 to 10 microvolts), (2)reasonable optical pumping, and (3) a greater frequency bandwidth.

In embodiments, various analyses are conducted to determine the improvedconversion rate when using the multilayer graphene structure as aquantum modulator, This includes: (1) determining the conversion ratebased on the microwave frequency for different electron densities, (2)determining the conversion rate based on the microwave driving voltage,(3) determining the conversion rate based on the optical pump amplitudeand the multilayer graphene length, and/or (4) determining conversionrate with decaying optical and microwave fields. Thus, an improvedconversion rate of the number of converted photons from the microwaveinput occurs with a graphene structure that has lower microwave drivingvoltages, a smaller graphene length, wider microwave frequency range,and reasonable pump amplitudes.

FIG. 1 describes an example design for graphene structure 100. Inembodiments, graphene structure 100 is electrically driven by amicrowave signal of frequency f_(m) and subjected to an optical inputpump of frequency f1 as shown in FIG. 1 . In embodiments, graphenestructure 100 is connected in an interdigital configuration and anoptical input pump is applied normally to the graphene layers withingraphene structure 100 and propagates in the direction of the x axiswith a total length 102. In embodiments, each layer 104 within graphenestructure 100 is located a distance 106 from each other layer 104.

FIG. 2 describes an example model capacitance design 200. Inembodiments, capacitance design 200 may be associated with graphenestructure 100 described in FIG. 1 and model graphene structure 100 as acapacitor. In embodiments, a particular number of identical graphenelayers 202 (e.g., “N” number) can be conceived as 2N-2 shunted identicalcapacitors 204 (each of capacitance C=2^(ε0ε/d)) as shown in FIG. 2 .Here c is the permittivity of the filling material. In embodiments, thetotal capacitance (per unit area) is given by CT=(2N−2)C=4(N−1)ε0/ε.

In embodiments, to determined modulated optical conductivity, amultilayer graphene structure (e.g., graphene structure 100) can bemodeled by the means of effective permittivity. In embodiments, thegraphene conductivity is conducted by both interband and intrabandmechanisms, given by equation 1:

$\sigma_{s} = {{\frac{{iq}^{2}}{4{\pi\hslash}}\ln\left( \frac{{2{\mu}_{C}} - {\left( {f + {i\tau^{- 1}}} \right)\hslash}}{{2{\mu}_{C}} + {\left( {f + {i\tau^{- 1}}} \right)\hslash}} \right)} + {\frac{{iq}^{2}K_{B}T}{{\pi\hslash}^{2}\left( {f + {i\tau^{- 1}}} \right)}{\left( {\frac{{\mu}_{C}}{K_{B}T} + {2\ln\left( {e^{- \frac{{\mu}_{C}}{K_{B}T}} + 1} \right)}} \right).}}}$

In embodiments, equation 1 includes one term that describes theinterband conductivity and a second term represents the intrabandconductivity. In embodiments, q is the electron charge, n is the plank'sconstant, τ is the scattering relaxation time, KB represents theBoltzman constant, T is the temperature, f is the frequency, and μ_(c)expresses the graphene chemical potential. In embodiments, the operationtemperature is considered at the cryogenic level (e.g., 3 milli-Kelvin).In embodiments, the graphene conductivity at a cryogenic-leveltemperature is dominated by the interband mechanism, while the intrabandconverge to Drude model.

In embodiments, a graphene chemical potential is given by equation 2 as:

$\mu_{C} = {\hslash V_{f}\sqrt{{{\pi n_{0}} + {\frac{2C_{T}}{q}v_{m}}},}}$

In embodiments, where no is the electron density per unit area,V_(f)=106 m/s, which is the Fermi velocity of the Dirac fermions, andν_(m) is the driving microwave voltage, defined by equation 3 (wheref_(m) is the microwave frequency and c.c. is a complex conjugate):

ν_(m) =ve ^(−i2πf) ^(in) ^(t) +c.c.

In embodiments, the microwave voltage in equation 3 is substituted inequation 2. Furthermore, using the approximation (1+λ)^(1/2)≈1+λ forλ«1, the chemical potential for 2CT ν«πn0q, can be determined inequation 4 as:

μ_(C) = μ_(C)^(′) + vμ_(C)^(″)e^(−i2πf_(m)i) + c.c., where${\mu_{C}^{\prime} = {{\hslash V}_{f}\sqrt{\pi n_{0}}}},{{{and}\mu_{C}^{''}} = {{\hslash V}_{f}{\frac{C_{T}}{q\sqrt{\pi n_{0}}}.}}}$

In embodiments, substituting the chemical potential in equation 4 intothe conductivity portion of equation 1 substituting the chemicalpotential in equation 4 into the conductivity expression in Eq. (1), andfor νμ_(c)«μ_(c)′, the graphene's conductivity can be approximated up tothe first order as equation 6:

σ_(s)=σ′_(s)+νσ″_(s) e ^(−f2πf) ^(m) ^(t) +c.c.

with equations 7 and 8 are:

$\sigma_{s}^{\prime} = {{\frac{{iq}^{2}}{4{\pi\hslash}}\ln\left( \frac{{2{\mu}_{C}^{\prime}} - {\left( {f + {i\tau^{- 1}}} \right)\hslash}}{{2{\mu}_{C}^{\prime}} + {\left( {f + {i\tau^{- 1}}} \right)\hslash}} \right)} + {\frac{{iq}^{2}K_{B}T}{{\pi\hslash}^{2}\left( {f + {i\tau^{- 1}}} \right)}\left( {\frac{{\mu}_{C}^{\prime}}{K_{B}T} + {2\ln\left( {e^{- \frac{{\mu}_{C}^{\prime}}{K_{B}T}} + 1} \right)}} \right)}}$$\sigma_{s}^{''} = {{\frac{{iq}^{2}}{\pi\hslash}\frac{\left( {f + {i\tau^{- 1}}} \right)\hslash}{{4\left( {\mu}_{C}^{\prime} \right)^{2}} - {\left( {f + {i\tau^{- 1}}} \right)^{2}\hslash^{2}}}{\mu}_{C}^{''}} + {\frac{{iq}^{2}K_{B}T}{{\pi\hslash}^{2}\left( {f + {i\tau^{- 1}}} \right)}\tanh\left( \frac{{\mu}_{C}^{\prime}}{K_{B}T} \right){\frac{{\mu}_{C}^{''}}{K_{B}T}.}}}$and vσ_(s)^(″) ≪ σ_(s)^(′).

In embodiments, the dispersion relation of a graphene structure (e.g.,graphene structure 100) may be given by equation 9 (with β is thepropagation constant and Z₀ is the free space impedance):

${\cos\left( {d\beta} \right)} = {{\cos\left( {d\sqrt{\varepsilon}\frac{2\pi f}{c}} \right)} - {i\frac{Z_{0}}{2\sqrt{\varepsilon}}\sin\left( {d\sqrt{\varepsilon}\frac{2\pi f}{c}} \right)\sigma_{S}}}$

Based on equation 6, the propagation constant can be given in equation10 as:

β=β′+νβ″e ^(−i2πf) ^(m) ^(t) +c.c.

In embodiments, the propagation constant from equation 10 is substitutedin the dispersion relation in equation 9 and expand nonlinear terms. Inembodiments, β′ may satisfy the dispersion relation in equation 9 withσ_(s)′ in lieu of σ_(s). In embodiments, β″ may be given by equation 11:

$\beta^{''} = {i\frac{Z_{0}}{2d\sqrt{\varepsilon}}\frac{\sin\left( {d\frac{2\pi f\sqrt{\varepsilon}}{c}} \right)}{\sin\left( {d\beta^{\prime}} \right)}{\sigma_{s}^{''}.}}$

Thus, based on equation 11, the effective permittivity of the graphenestructure is given by equation 12:

ε_(eff) _(j) =ε′_(eff) _(j) +νε_(eff) _(j) ″e ^(−i2πf) ^(m) ^(t) +c.c.

and where equation 13 is:

${\varepsilon_{{eff}_{i}}^{\prime} = \left( \frac{\beta_{j}^{\prime}}{k_{0_{j}}} \right)^{2}},{{{and}\varepsilon_{{eff}_{i}}^{''}} = {2\frac{\beta_{j}^{\prime}\beta_{j}^{''}}{k_{0_{j}}^{2}}}}$

In embodiments, as shown in equation 12, the microwave signal modulatesthe effective permittivity of the graphene structure. In embodiments,the upper and lower sidebands are generated with frequencies f2=f1+f_(m)and f3=f1−fm, respectively. In embodiments, the destruction resonance ofthe multilayer graphene occurs at f3 so that the lower side band issuppressed to the maximum level. Thus, the spontaneous process isminimized. In embodiments, the group velocity at the destructionresonance frequency is set at zero, similar to the reflection resonancefor externally incident optical waves. However, in the current scenariothere are no reflected waves as the lower side band is generated withinthe graphene layers and the layered medium is reciprocal. As such, thelower sideband is suppressed by setting d=c/(f₃(ε)^(1/2)). Inembodiments, a medium transmittance may be determined to quantify thesuppression of the lower sideband. Thus, optical fields in the graphenestructure are given by equation 14 (with u_(j) is the slow varyingamplitude and j ∈ {1, 2} as:

{right arrow over (E)} _(j) =u _(j)(e ^(−i2πf) ^(m) ^(t) +c.c.)ê _(y).

In embodiments, a classical Hamiltonian for equation 15:

=½∫_(ν)(ε₀ε_(eff) |{right arrow over (E)} _(t)|²+μ₀ |{right arrow over(H)} _(t)|²)∂V.

In embodiments, E_(t) is the total electric field, H_(t) represents thetotal magnetic field, and V is the volume. In embodiments, theHamiltonian in equation 15 describes the total electromagnetic energy ofthe system. In embodiments, the first part represents the total electricfield taking into account the effective permittivity, as described inequation 12. In embodiments, the second part of equation 15 takes intoaccount the magnetic energy, while the system of the graphene structurehas zero magnetic susceptibility. In embodiments, the effectivepermittivity is approximated by implementing a perturbation approachconsidering a weak driving microwave voltage (e.g., ranging from 1 to 10microvolts). Accordingly, the chemical potential (represented by itsexpansion) can be approximated up to the first order. This is validatedby imposing the condition 2CT ν πn0q. Consequently, the grapheneconductivity, and the effective permittivity can be approximated up tothe first order. This approach is verified when numerical calculationsare carried out. In embodiments, substituting the expressions of thepropagating fields in equation 14 into the Hamiltonian expression inequation 15, and using the effective permittivity in equation 12, theHamiltonian expression can be rewritten as 2CTv «πn0q.

In embodiments, the graphene conductivity, and the effectivepermittivity can be approximated up to the first order. In embodiments,substituting the expressions of the propagating fields in equation 14into the Hamiltonian expression in equation 15, and using the effectivepermittivity in equation 12, the Hamiltonian expression can be rewrittenas equation 16:

=H ₀ +H ₁,

where equation 17 is:

$\mathcal{H}_{0} = {{\sum\limits_{j = 1}^{2}{\varepsilon_{{eff}_{j}}^{\prime}\varepsilon_{0}{\mathcal{u}}_{j}^{*}{\mathcal{u}}_{j}}} + {c.c.}}$

And equation 18 is:

H ₁=

ε″_(eff2)ε₀ u ₁ *ν*u ₂ +c.c.

In embodiments, as shown in equation 18, H₀ are the classical freefields Hamiltonian and H₁ is the classical interaction Hamiltonian. Inembodiments, these expressions are used to describe the quantumevolution of the interacting fields.

In embodiments, the optical and microwave fields can be quantizedthrough the following relations (equation 19a and equation 19b):

${u_{j} = {\left( \frac{\hslash f_{j}}{\varepsilon_{{eff}_{j}}^{\prime}\varepsilon_{0}} \right)^{\frac{1}{2}}{\hat{a}}_{j}}},{{{and}v} = {\left( \frac{\hslash f_{m}}{C_{T}} \right)^{\frac{1}{2}}\hat{b}}}$

In embodiments, where a{circumflex over ( )}j and b{circumflex over ( )}are the annihilation operators of the jth optical mode and the microwavemode, respectively. In embodiments, the quantum Hamiltonian can beobtained by substituting the annihilation (and creation) operators,defined above, into the classical Hamiltonian in equation 16, yieldingequation 20:

=Ĥ ₀ +Ĥ ₁,

where equation 21 is:

Ĥ ₀ =ℏf _(m) {circumflex over (b)} ^(†) {circumflex over (b)}+ℏf ₁ â ₁^(†) â ₁ +ℏf ₂ â ₂ ^(†) â ₂,

and equation 22 is:

Ĥ ₁ =ℏg(â ₂ ^(†) {circumflex over (b)}â ₁ +h.c.)

In embodiments, where h.c. is the Hermitian conjugate and g is theconversion rate given by equation 23:

$g = {\varepsilon_{{eff}_{2}}^{''}\sqrt{\frac{f_{1}f_{2}}{\varepsilon_{{eff}_{1}}^{\prime}\varepsilon_{{eff}_{2}}^{\prime}}}\sqrt{\frac{\hslash f_{m}}{C_{T}}}}$

In embodiments, substituting quantum Hamiltonian expression of equation20 into Heisenberg equations of motions that yield equations 24, 25, and26:

$\frac{\partial{\hat{a}}_{1}}{\partial t} = {{{- i}f_{1}{\hat{a}}_{1}} - {{ig}{\hat{b}}^{\dagger}{\hat{a}}_{2}}}$$\frac{\partial{\hat{a}}_{2}}{\partial t} = {{{- i}f_{2}{\hat{a}}_{2}} - {{ig}\hat{b}{\hat{a}}_{1}}}$$\frac{\partial\hat{b}}{\partial t} = {{{- i}f_{m}\hat{b}} - {{ig}{\hat{a_{1}}}^{\dagger}{\hat{a}}_{2}}}$

In embodiments, In this work, the optical pump input a{circumflex over( )}₁ is considered intensive and treated classically. In embodiments,on using the rotation approximation:

(â _(j) =Â _(j) e ^(−iω) ^(j) ^(t) and {circumflex over (b)}={circumflexover (B)}e ^(−iω) ^(M) ^(t)).

the equations of motion are given by equations 27 and 28 as:

$\frac{\partial{\hat{A}}_{2}}{\partial t} = {{- {igA}_{1}}\hat{B^{\prime}}}$$\frac{\partial\hat{B}}{\partial t} = {{- {igA}_{1}^{*}}\hat{A_{2}}}$

In embodiments, the solutions of equations 27 and 28 are given byequation 29:

Â ₂(t)=Â ₂(0)cos(g|A ₁ |t)−ie^(−iϕ) ⁰ {circumflex over (B)}(0)sin(g|A ₁|t)

In embodiments, φ₀ is the phase of the optical input A1. In embodiments,using, equation 29, if the interaction time satisfies equation 30:

${g{❘A_{1}❘}t} = \frac{\pi}{2}$

Where the upper sideband is

-   -   Â₂,        And the microwave signal is    -   {circumflex over (β)}        Such that the quantum state of the optical upper sided band        depends only on the state of the microwave signal, thus        achieving a quantum microwave-to-optical conversion.

FIGS. 3 and 4 show example electronic graphs of numerical analysisassociated with equations 1 to 30. In embodiments, air is fillingmaterial, the optical lower sideband frequency is fixed at f₃=193.5484THz, and the separation distance between graphene layers is given byd=1.55 μm. In embodiments, the frequency of the optical pump f₁ (whichis between f₂ and f₃) and the microwave signal frequency fm are variedaccordingly. In embodiments, the area of the graphene layers is 1 mm².

In embodiments, the propagation constant (and the group velocity) arecalculated for the graphene structure. In embodiments, the transmittanceT of the medium is simulated (e.g., using the transfer matrix method) toquantify the suppression of the lower sideband and an extraction ratiois calculated. As shown in FIG. 3 , the propagation constant and thegroup velocity (i.e., vg) are shown versus optical frequency. An exampleof f₁, f₂, and f₃ are shown for f_(m)=50 GHz. Here, ν_(g) is defined by:

$v_{g} = {\frac{\partial f}{\partial\beta}.}$

As shown in FIG. 4 , the transmittance is displayed versus the opticalfrequency, considering different numbers of graphene layers. Theextraction ratio between the upper and lower side bands can be definedas:

$\eta_{E} = \frac{{T^{2}(N)}❘_{f = f_{3}}}{{T^{2}(N)}❘_{f = f_{2}}}$

As further shown in FIG. 4 , the number of layers is needed to reach areasonable extraction ratio is shown. For example, for fm=50 GHz, theextraction ratio equals ηE=1.1 for N=100, ηE=3 for N=300, and ηE=32 forN=1000.

In embodiments, the conversion rate is characterized using differentparameters including the drive microwave voltage, the microwavefrequency, the electron densities, and the medium length. As shown inFIG. 5 , the conversion rate g is evaluated versus the microwavefrequency. Here, N=1000, ν=1 μV, and different electron densities no areconsidered. Higher conversion rates can be achieved for smaller electrondensities. In embodiments, the electron density may satisfy a thresholdvalue given by 2C_(TV) «πn₀q. As shown in FIG. 5 , (A) is n₀=2×10¹² m⁻²,(B) is n₀=3×10¹² m⁻², and (C)=n₀=5×10¹² m⁻².

In FIG. 6 , the conversion rate is shown versus the driving microwavevoltage. Here, N=1000, and n₀=2×10¹² m⁻². Significant conversion ratescan be achieved for microvolt ranges. This is due to the dispersionproperty of the multilayer graphene and to the significant variation ofthe graphene conductivity in response to even very small drivingelectric voltages.

In embodiments, the length of the multilayer graphene medium is given byL=(N−1)d. Consequently, by using t=L 1/ν_(g) in equation 30, therequired optical pump amplitude is shown by equation 31 as:

${❘A_{1}❘} = \frac{\pi v_{g}}{2L{❘g❘}}$

In FIG. 7 , the conversion rate g is displayed versus the graphenemedium length L and the pump amplitude A₁. As can be seen, significantconversion rates can be achieved for few propagated millimeters, yetwith reasonable pump amplitudes.

In embodiments, equations of motion in equations 27 and 28 describe aclosed-quantum system. However, both the optical and the microwavefields decay with time. In embodiments, optical decay is attributed toattenuation and reflection of the multilayer graphene, modeled byincluding the time decay parameter F in the equations of motion. Theattenuation optical time decay rate is defined by:

Γ_(A)=2ν_(g) Im(β).

In embodiments, the reflection of the multilayer graphene may be modeledby an equivalent decay coefficient Γ_(R). This decay coefficient (wecalled it reflection decay coefficient) can be defined by setting exp(−t₀Γ_(R))=T₀ ². In embodiments, T₀ is transmittance of a single blockof the multilayer graphene (composed of d filling material and a singlegraphene layer), and t₀=d/ν_(g) is the total flight time over a singleblock.

In embodiments, given that ν and b{circumflex over ( )} are linearlyrelated as shown in equation 19, modelling the microwave decay rate isconducted. First, the microwave rms power losses is calculated byν²/2R_(g) where Rg=Re(1/σ_(s)) is the graphene resistance for a squarelayer. Here, the graphene conductivity is calculated at the microwavefrequency and T=3mK.

Second, the microwave energy at a time, let us say t₀, is approximatedas the initial energy at time t=0 minus the rms dissipated energy, thatis:

${qv} - {\frac{v^{2}}{2R_{g}}t_{0}}$

In embodiments, the effective microwave decay rate Γm is introduced tocalculate the microwave energy at the same time t₀, yielding:

${{qv} - {\frac{v^{2}}{2R_{g}}t_{0}}} = {qve}^{{- \frac{\Gamma_{m}}{2}}t_{0}}$

It then follows:

$\Gamma_{m} = {{- \frac{2}{t_{0}}}\ln\left( {1 - \frac{{vt}_{0}}{2{qR}_{S}}} \right)}$

We note here that Γm depends on the applied voltage amplitude as theelectrical dissipation is a nonlinear process. In FIG. 8 , the opticaland the microwave decay time rates are presented versus the microwavefrequency. Here, f3 is fixed at the destruction resonance, and f1 isadjusted in accordance to fm, as f1=f3+fm, n0=2×1012m−2, and ν=1μν.Accordingly, the motions of equations (equations 32 and 33):

∂Â ₂/∂_(t)=−Γ/2 Â ₂ −igA ₁{circumflex over (β)}+√{square root over (ΓN₂)},

$\frac{\partial\hat{B}}{\partial t} = {{{- \frac{\Gamma_{m}}{2}}\hat{B}} - {{igA}_{1}^{*}{\hat{A}}_{2}} + {\sqrt{\Gamma_{m}}N_{m3}}}$

where Γ=ΓA+ΓR is the total optical decay coeÿcient, Γm represents themicrowave decay coefficient, and ΓR=vg/d(ln(1/T₀ ²). Here, N2 and Nm arethe quantum Langevin noise operators, obeying:

$\left\lbrack {{N\left( t_{1} \right)},{N\left( t_{2} \right)}^{\dagger}} \right\rbrack = {{{\delta\left( {t_{1} - t_{2}} \right)}{and}\left\langle {{N\left( t_{1} \right)}^{\dagger}{N\left( t_{2} \right)}} \right\rangle} = {\frac{1}{\exp\left( {{\hslash f}/k_{B}T} \right)}{{\delta\left( {t_{1} - t_{2}} \right)}.}}}$

In embodiments, the dissipation characterized by the time decay rates Γand Γm are included in the equations of motions (equations 32 and 33).Hence, according to the fluctuation-dissipation theorem, the Langevinforces are included. The langevin forces represent the noise in themicrowave and optical frequencies as the feed-back of the environment tothe system. In embodiments, squeezing between different frequency fieldsdue to a spontaneous process is ignored. In embodiments, the reflectedoptical pump may be modulated by the microwave signal. In embodiments,as the layered structure is reciprocal, the reflected optical pump mayoperate the same dynamics as the transmitted optical pump and modulationof the side bands is neglected. Accordingly, to evaluate the number ofconverted photons, one may write the evolution equations for the meanoptical (equation 34) and microwave (equation 35) fields:

${\frac{\partial{\hat{A}}_{2}}{\partial t} = {{{- \frac{\Gamma}{2}}{\hat{A}}_{2}} - {{igA}_{1}\hat{B}}}},$$\frac{\partial\hat{B}}{\partial t} = {{{- \frac{\Gamma_{m}}{2}}\hat{B}} - {{igA}_{1}^{*}{\hat{A}}_{2}}}$

In embodiments, using equation 31, a complete set of differentialequations describe the numbers of photon evolution. In addition,Heaviside step pump switching function H(t), the system of thedifferential equations can be solved and the solutions is:

$\begin{matrix}{{\hat{A}}_{2}^{\dagger}{\hat{A}}_{2}} & \left( {{solution}x} \right)\end{matrix}$ $\begin{matrix}{{\hat{B}}^{\dagger}\hat{B}} & \left( {{solution}y} \right)\end{matrix}$

In embodiments, solution x may contain terms that correlate with themicrowave state and others that decorrelated with microwave state. Inembodiments, the signal to noise ratio (SNR) is defined as the ratio ofthe terms correlate with microwave state to those that decorrelated withmicrowave state. On imposing the condition of

${A = \left( \frac{\Gamma - \Gamma_{m}}{4g} \right)},$

the parameter α approaches zero which implies a large SNR. Thus, thedecorrelate terms can be ignored. Accordingly, the solution x can begiven as equation 36:

${{{{\hat{A}}_{2}^{\dagger}{\hat{A}}_{2}} = {{Agte}^{- \frac{t({\Gamma + \Gamma_{m}})}{4}}{\hat{A}}_{2}^{\dagger}\hat{B}}}❘}_{t = 0}$

Where t=L/ν_(g) is the interaction. In embodiments, the optical andmicrowave fields can be considered decorrelated at t=0 and equation 37is:

${{{{{{\hat{B^{\dagger}}{\hat{A}}_{2}}❘}_{t = 0} = \hat{B^{\dagger}}}❘}_{t = 0}{\hat{A}}_{2}}❘}_{t = 0} \simeq \sqrt{{{{{{\hat{A}}_{2}^{\dagger}{\hat{A}}_{2}}❘}_{t = 0}\hat{B^{\dagger}}\hat{B}}❘}_{t = 0}}$

In embodiments, the SNR becomes in equation 38:

${SNR} = \frac{{\hat{B}❘}_{t = 0}}{{{\hat{A}}_{2}❘}_{t = 0}}$

As shown in equation 38, the SNR is large, given that the numerator isthe initial microwave expectation value of the annihilation operator,while the denominator is initially at the noise level. For example, amicrowave voltage signal of ν=1 μV, the SNR is greater than 30 dB.

FIG. 9 , is an example electronic graph that indicates the number ofconverted photons versus the frequency of the microwave signal. Inembodiments, a significant number of optical photons are converted overa wide microwave frequency range. In embodiments, different lengths ofgraphene structures (with layers N) are considered. These include L=1.54mm (i.e., N=1000), L=1.23 mm (i.e., N=800), and L=1.08 (i.e., N=700). Inembodiments, a larger number of converted photons may be achieved forshorter lengths of multilayer graphene. However, in this case, largeroptical pump amplitudes are required and smaller (extra)ction ratiosresult. For example, for 1.23 mm and 1.08 mm, respectively. Thecorresponding pump amplitudes are A1=5.36×10³, 6.27×10³, and 6.92×10³,while the extraction ratios are ηE=31, 20, and 16, respectively. Here,the classical slow varying field amplitude of the optical pump field,i.e., u1, can be calculated from the pump operator, i.e., A1, byequation 19.

In embodiments, as required by the developed model, u1 values are ofmoderate level. For example, in FIG. 9 , A1=6.92×10³ for fm=20 GHz andL=1.08 mm medium length. The corresponding electric optical pump fieldintensity is u1=71 104 V/m. Thus, the optical pump can be safely treatedclassically and in the same time its intensity is below the damagethreshold of graphene. In embodiments, the peak of the number ofconverted photons in FIG. 9 is attributed to the transmittance responseof the layered media. In embodiments, the optical decay coefficient, Γ,is compressed of the absorption decay coefficient ΓA and the reflectiondecay coefficient ΓR. Thus, the transmittance (or equivalently thereflection) of the layer medium is dispersive and depends on thefrequency of the converted photons (which is f3=f1+fm). This can beverified by comparing the transmittance response, versus fm, with thenumber of photons in FIG. 9 .

FIG. 10 is a diagram of example components of a device 1000. Device 1000may correspond to a computing device, such as devices 1100, 1200, and/or1202. Alternatively, or additionally, devices 1100, 1200, and/or 1202may include one or more devices 1000 and/or one or more components ofdevice 1000.

As shown in FIG. 10 , device 1000 may include a bus 1010, a processor1020, a memory 1030, an input component 1040, an output component 1050,and a communications interface 1060. In other implementations, device1000 may contain fewer components, additional components, differentcomponents, or differently arranged components than depicted in FIG. 10. Additionally, or alternatively, one or more components of device 1000may perform one or more tasks described as being performed by one ormore other components of device 1000.

Bus 1010 may include a path that permits communications among thecomponents of device 1000. Processor 1020 may include one or moreprocessors, microprocessors, or processing logic (e.g., a fieldprogrammable gate array (FPGA) or an application specific integratedcircuit (ASIC)) that interprets and executes instructions. Memory 1030may include any type of dynamic storage device that stores informationand instructions, for execution by processor 1020, and/or any type ofnon-volatile storage device that stores information for use by processor1020. Input component 1040 may include a mechanism that permits a userto input information to device 1000, such as a keyboard, a keypad, abutton, a switch, voice command, etc. Output component 1050 may includea mechanism that outputs information to the user, such as a display, aspeaker, one or more light emitting diodes (LEDs), etc.

Communications interface 1060 may include any transceiver-like mechanismthat enables device 1000 to communicate with other devices and/orsystems. For example, communications interface 1060 may include anEthernet interface, an optical interface, a coaxial interface, awireless interface, or the like.

In another implementation, communications interface 1060 may include,for example, a transmitter that may convert baseband signals fromprocessor 1020 to radio frequency (RF) signals and/or a receiver thatmay convert RF signals to baseband signals. Alternatively,communications interface 1060 may include a transceiver to performfunctions of both a transmitter and a receiver of wirelesscommunications (e.g., radio frequency, infrared, visual optics, etc.),wired communications (e.g., conductive wire, twisted pair cable, coaxialcable, transmission line, fiber optic cable, waveguide, etc.), or acombination of wireless and wired communications.

Communications interface 1060 may connect to an antenna assembly (notshown in FIG. for transmission and/or reception of the RF signals. Theantenna assembly may include one or more antennas to transmit and/orreceive RF signals over the air. The antenna assembly may, for example,receive RF signals from communications interface 1060 and transmit theRF signals over the air, and receive RF signals over the air and providethe RF signals to communications interface 1060. In one implementation,for example, communications interface 1060 may communicate with anetwork (e.g., a wireless network, wired network, Internet, etc.).

As will be described in detail below, device 1000 may perform certainoperations. Device 1000 may perform these operations in response toprocessor 1020 executing software instructions (e.g., computerprogram(s)) contained in a computer-readable medium, such as memory1030, a secondary storage device (e.g., hard disk, CD-ROM, etc.), orother forms of RAM or ROM. A computer-readable medium may be defined asa non-transitory memory device. A memory device may include space withina single physical memory device or spread across multiple physicalmemory devices. The software instructions may be read into memory 1030from another computer-readable medium or from another device. Thesoftware instructions contained in memory 1030 may cause processor 1020to perform processes described herein. Alternatively, hardwiredcircuitry may be used in place of or in combination with softwareinstructions to implement processes described herein. Thus,implementations described herein are not limited to any specificcombination of hardware circuitry and software.

FIG. 11 is an example diagram. FIG. 11 describes device 1100,communication 1102, and communication 1104. In embodiments, device 1100may a computing device with features/structures similar to thatdescribed in FIG. 10 . In embodiments, device 1100 may be a computingdevice that is part of a laptop, desktop, tablet, smartphone, and/or anyother device that may receive communication 1102, analyze communication1102, and generate output 1104 based on communication 1102. As shown inFIG. 11 , communication 1102 may be received by device 1100 (e.g., viakeyboard inputs, touchscreen inputs, voice inputs, etc.). Inembodiments, communication 1102 may include information about a graphenestructure, such as number of layers, thickness, distance between layers,electric features, dielectric features, etc. In embodiments, device 1100may receive communication 1102 and, based on one or more of equations 1to 38, that generate output 1104 that includes information aboutmicrowave voltage that may provide for the maximum conversion rate ofthe microwave fields to optical photons. In alternate embodiments,device 1100 may include a mechanism that receives communication 1102 andgenerates microwave voltage as part of output 1104.

FIG. 12 is an example diagram. FIG. 12 describes device 1200, device1202, input 1204, and output 1206. In embodiments, device 1200 may acomputing device with features/structures similar to that described inFIG. 12 . In embodiments, device 1200 may be a computing device that ispart of a laptop, desktop, tablet, smartphone, and/or any other devicethat may receive communication 1202, analyze communication 1204, andgenerate output 1206 based on communication 1204. In embodiments, device1200 may be a computing device that is part of a laptop, desktop,tablet, smartphone, and/or any other device that may receivecommunication 1204, analyze communication 1204, and generate output 1206based on communication 1204. In embodiments, device 1202 may be acomputing device that is part of a laptop, desktop, tablet, smartphone,and/or any other device that may receive output 1206, analyze output1206, and generate output 1208 based on output 1206.

In embodiments, communication 1204 may include microwave fieldinformation based on one or more of equations 1 to 38. In embodiments,device 1200 may receive communication 1204 and analyze communication1204 based on one or more equations 1 to 38. In embodiments, device 1200may generate output 1206. In embodiments, output 1206 may includeelectronic design information for a graphene structure. In embodiments,output 1206 may be received by device 1202. In embodiments, device 1202may generate a physical graphene structure (e.g., graphene structure100). In embodiments, device 1202 may include wafer fabrication systems.In embodiments, device 1202 may generate a graphene structure or acomposite structure that includes a graphene structure.

Even though particular combinations of features are recited in theclaims and/or disclosed in the specification, these combinations are notintended to limit the disclosure of the possible implementations. Infact, many of these features may be combined in ways not specificallyrecited in the claims and/or disclosed in the specification. Althougheach dependent claim listed below may directly depend on only one otherclaim, the disclosure of the possible implementations includes eachdependent claim in combination with every other claim in the claim set.

While various actions are described as selecting, displaying,transferring, sending, receiving, generating, notifying, and storing, itwill be understood that these example actions are occurring within anelectronic computing and/or electronic networking environment and mayrequire one or more computing devices, as described in FIG. 10 , tocomplete such actions. Furthermore, it will be understood that thesevarious actions can be performed by using a touch screen on a computingdevice (e.g., touching an icon, swiping a bar or icon), using akeyboard, a mouse, or any other process for electronically selecting anoption displayed on a display screen to electronically communicate withother computing devices. Also it will be understood that any of thevarious actions can result in any type of electronic information to bedisplayed in real-time and/or simultaneously on multiple user devices.For FIGS. 3 to 9 , the electronic graphs may be generated by a computingdevice, such as device 1000, and displayed via a graphical user device(GUI).

No element, act, or instruction used in the present application shouldbe construed as critical or essential unless explicitly described assuch. Also, as used herein, the article “a” is intended to include oneor more items and may be used interchangeably with “one or more.” Whereonly one item is intended, the term “one” or similar language is used.Further, the phrase “based on” is intended to mean “based, at least inpart, on” unless explicitly stated otherwise. Also, the phrase“converted text,” or “converted information” may indicate informationthat has been converted from handwritten or non-handwritten informationto printed information. The phrase “information” may indicate letters,words, numbers, and/or symbols. The phrase “text” may indicate letters,numbers, and/or symbols. The phrases “information” and “text” mayindicate the same thing, i.e., letters, numbers, and/or symbols. Also,while the above examples are associated with prescriptions, pharmacists,and doctors, the above example actions may also be used for otherscenarios and analysis of other types of handwritten text, such as withpurchase orders, shipping orders, etc.

In the preceding specification, various preferred embodiments have beendescribed with reference to the accompanying drawings. It will, however,be evident that various modifications and changes may be made thereto,and additional embodiments may be implemented, without departing fromthe broader scope of the invention as set forth in the claims thatfollow. The specification and drawings are accordingly to be regarded inan illustrative rather than restrictive sense.

What is claimed is:
 1. A graphene structure comprising: one or moregraphene layers, wherein the graphene structure: receives microvolts,wherein the microvolts are sent to the graphene structure via amicrowave signal, and the microwave signal is received by the graphenestructure at a quantum level, receives the microvolts at a particulartemperature, generates optical photons based on receiving themicrovolts; outputs the optical photons at the quantum level, wherein:the graphene structure is a quantum modulator that improves a conversionrate of the number of photons from the signal.
 2. The graphene structureof claim 1, wherein: the multiple graphene layers have a distance, d,from each other, and the multiple graphene layers are connected witheach other in an interdigital configuration.
 3. The graphene structureof claim 2, wherein the graphene structure operates electronically as acapacitor and, at the same time, operate optically as a periodic medium,and wherein each of the graphene layers has an area of 1 mm².
 4. Thegraphene structure of claim 1, where the graphene structure has multiplegraphene layers, wherein each of the multiple graphene layers has alength, L, wherein the length is less than 2.0 millimeters.
 5. Thegraphene structure of claim 1, wherein the graphene structure receives adriving voltage that is less than 10 microvolts.
 6. The graphenestructure of claim 1, wherein the graphene structure is pumped by anoptical pump, wherein: the optical pump has an intensity level that isbelow a damage threshold level of the graphene structure.
 7. Thegraphene structure of claim 1, wherein the graphene structure generatesa lower sideband.
 8. The graphene structure of claim 7, wherein thegraphene structure suppresses the lower sideband generated when thegraphene structure is pumped by an optical pump.
 9. The graphenestructure of claim 7, wherein the graphene structure suppresses thelower sideband to a destruction resonance value associated with thegraphene structure.
 10. The graphene structure of claim 8, wherein thegraphene structure generates an upper sideband when the lower sidebandis generated.
 11. The electronic method of claim 1, wherein the graphenestructure has multiple graphene layers that are connected to each otherin an interdigital configuration.
 12. The graphene structure of claim 1,wherein a conversion rate, associated with generating the opticalphotons from the microvolts, is based on a length of the graphenestructure and the optical pump amplitude.
 13. A graphene structurecomprising: one or more graphene layers, wherein the graphene structure:receives microvolts, wherein the microvolts are sent to the graphenestructure via a microwave signal, and the microwave signal is receivedby the graphene structure at a quantum level, receives the microvolts ata particular temperature, generates optical photons based on receivingthe microvolts; and outputs the optical photons at the quantum level.14. The graphene structure of claim 13, wherein the graphene structurehas a zero magnetic susceptibility.
 15. The graphene structure of claim13, wherein each of the one or more graphene layers has a particularcapacitance.
 16. The graphene structure of claim 13, wherein thegenerated lower sideband is suppressed by a multilayer graphenedestruction resonance associated with the graphene structure.
 17. Thegraphene structure of claim 16, wherein low noise conversion isassociated with the suppression of the lower sideband.
 18. The graphenestructure of claim 13, wherein the graphene structure has a conversionrate associated with a number of converted photons from a microwaveinput.
 19. The graphene structure of claim 18, wherein the conversionrate is based on the microwave driving voltage.
 20. The graphenestructure of claim 18, wherein the conversion rate is based on decayingoptical and microwave fields.